While the cerebellum appears to be involved in a multitude of tasks [1], it has a relatively invariant local neural circuitry, which is well preserved across different functional regions and different species. This has given rise to the idea that the cerebellar circuit subserves a single computational function across tasks — the universal cerebellar transform [2]. In this review, we will critically examine this idea across three different motor domains.

At the circuit level, cerebellar information processing is well understood. More than 50 years ago Marr, Albus, and Ito 3, 4, 5 formulated a hypothesis of circuit-level function that, at least in its main tenets, has stood the test of time. Glancing over many physiological details (Figure 1), the cerebellum transforms a mossy fiber input (X) into Purkinje cell activity (W) that then modulates activity in the cerebellar nuclei, which ultimately conveys the cerebellar output (Y). The main idea is that the circuit of cerebellum is uniquely suited to learn complex functions YF(X) based on a relatively sparse teaching signal — the climbing fiber input from the inferior olive (Z) 5, 6, 7.

The circuit has a number of special features that endow it with a special capacity to learn. First, the mossy fiber input is distributed on a simply astounding number of granule cells, each of which integrates four to five mossy fiber inputs in a nonlinear manner [8]. This arrangement may give the cerebellum the ability to learn very high-dimensional functions of the input 5, 9. This massively expanded input signal is then relayed to the large Purkinje cells, which receives >175 000 inputs via parallel fibers. Each Purkinje cell also receives typically one climbing fiber which provides a powerful plasticity-inducing input to the Purkinje cell. The climbing fiber input (Z) tunes the transformation of the mossy fiber input into Purkinje cell activity (W = G(X)), leading to the reduction in the simple spike (SS) firing rates of Purkinje cells (W), hence indirectly modulating the input–output relationship (YF(x)). Through long-term depression, Purkinje cells can learn to lower their SS firing rate in anticipation of the climbing fiber input in a temporal precisely tuned manner 10, 11. This reduction in SS rate leads to a disinhibition of the targeted deep cerebellar nuclei (DCN) cells, which also receive direct input from the mossy fibers. The output of the DCN goes to a multitude of targeted downstream structures, for example, brainstem motor nuclei or the thalamus. Additionally, each DCN circuit also sends inhibitory input to the inferior olive (IO) cells that send climbing fibers to the associated Purkinje cells. In this way, the circuit learns to predict climbing fiber input based on a high-dimensional input signal and automatically cancels this teaching signal when its occurrence was predicted.

The highly consistent nature of this circuitry has given rise to the idea that the cerebellum, when working with other brain structures to solve a specific task, also performs a unique common function, the so-called ‘universal cerebellar transform’ 2, 12. One of the most influential formulations of this idea is that it implements a forward model 13, 14, 15, 16. Here, the main idea is that the output of the cerebellum is used as a sensory prediction, which then can be used to be compared to the incoming sensory signal. The discrepancy between the two signals is then fed back to the system as an error signal via climbing fibers (Figure 2). Alternatively, the cerebellar output may serve as a motor command, that is, the cerebellum may constitute an inverse model 17, 18, 19. Other hypotheses have highlighted timing 20, 21, 22 or prediction as a general principle 23, 24, 25, 26, 27.

Even though our understanding of the local cerebellar circuitry is advancing every year, it has been extremely difficult to test these domain-general ideas of how this system works when it is put into the context of the brain-wide system to control a behavior. We will argue that the main reason for this failure is to appreciate the diversity of the nature of input–output mappings that the cerebellum performs. We will summarize the results of electrophysiological studies in relatively simple motor behaviors, which show that the nature of the mossy fiber input signal (X), of the teaching signal (Z), and the function of the output can vary dramatically across different tasks. Furthermore, we summarize recent evidence that the cerebellar circuit may fulfill different functions at multiple stages of even a single task. We argue that it is important to understand this multitude of functions rather than assuming a priori that all processes can be neatly summarized as subserving a single computational principle.